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arXiv · 2607.07867

An edge-bicolored graph approach to the Ising model on random regular graphs

Michael Borinsky·Shiyue Ren·Maximilian Wiesmann
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Abstract

We give an exact solution of the ferromagnetic Ising model on a random regular graph ensemble via analytic combinatorics. Expressing the partition function as the generating function of labeled edge-bicolored graphs, we obtain the free energy in the thermodynamic limit from the asymptotic enumeration of these graphs. A simple analysis of the resulting formula reveals a second-order phase transition with critical exponents of the mean-field universality class.

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Michael Borinsky, Shiyue Ren, Maximilian Wiesmann. 2026-07-08. An edge-bicolored graph approach to the Ising model on random regular graphs. https://arxiv.org/abs/2607.07867

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